2.51/2.51 MAYBE 2.51/2.51 2.51/2.51 DP problem for innermost termination. 2.51/2.51 P = 2.51/2.51 f10#(x1, x2, x3, x4) -> f9#(x1, x2, x3, x4) 2.51/2.51 f9#(I0, I1, I2, I3) -> f4#(0, 0, rnd3, I3) [rnd3 = rnd3] 2.51/2.51 f5#(I4, I5, I6, I7) -> f4#(I4, 0, I8, I7) [I7 <= 0 /\ y1 = 1 /\ I8 = I8] 2.51/2.51 f5#(I9, I10, I11, I12) -> f2#(I9, I10, I11, -1 + I12) [1 <= I12] 2.51/2.51 f8#(I13, I14, I15, I16) -> f3#(I13, I14, I15, I16) 2.51/2.51 f3#(I17, I18, I19, I20) -> f8#(I17, I18, I19, I20) 2.51/2.51 f2#(I25, I26, I27, I28) -> f5#(I25, I26, I27, I28) 2.51/2.51 f4#(I29, I30, I31, I32) -> f1#(I29, I30, I31, I32) 2.51/2.51 f1#(I33, I34, I35, I36) -> f3#(I33, I34, I35, I36) [1 <= I35] 2.51/2.51 f1#(I37, I38, I39, I40) -> f2#(0, I38, I39, rnd4) [I39 <= 0 /\ I41 = 1 /\ rnd4 = rnd4] 2.51/2.51 R = 2.51/2.51 f10(x1, x2, x3, x4) -> f9(x1, x2, x3, x4) 2.51/2.51 f9(I0, I1, I2, I3) -> f4(0, 0, rnd3, I3) [rnd3 = rnd3] 2.51/2.51 f5(I4, I5, I6, I7) -> f4(I4, 0, I8, I7) [I7 <= 0 /\ y1 = 1 /\ I8 = I8] 2.51/2.51 f5(I9, I10, I11, I12) -> f2(I9, I10, I11, -1 + I12) [1 <= I12] 2.51/2.51 f8(I13, I14, I15, I16) -> f3(I13, I14, I15, I16) 2.51/2.51 f3(I17, I18, I19, I20) -> f8(I17, I18, I19, I20) 2.51/2.51 f6(I21, I22, I23, I24) -> f7(I21, I22, I23, I24) 2.51/2.51 f2(I25, I26, I27, I28) -> f5(I25, I26, I27, I28) 2.51/2.51 f4(I29, I30, I31, I32) -> f1(I29, I30, I31, I32) 2.51/2.51 f1(I33, I34, I35, I36) -> f3(I33, I34, I35, I36) [1 <= I35] 2.51/2.51 f1(I37, I38, I39, I40) -> f2(0, I38, I39, rnd4) [I39 <= 0 /\ I41 = 1 /\ rnd4 = rnd4] 2.51/2.51 2.51/2.51 The dependency graph for this problem is: 2.51/2.51 0 -> 1 2.51/2.51 1 -> 7 2.51/2.51 2 -> 7 2.51/2.51 3 -> 6 2.51/2.51 4 -> 5 2.51/2.51 5 -> 4 2.51/2.51 6 -> 2, 3 2.51/2.51 7 -> 8, 9 2.51/2.51 8 -> 5 2.51/2.51 9 -> 6 2.51/2.51 Where: 2.51/2.51 0) f10#(x1, x2, x3, x4) -> f9#(x1, x2, x3, x4) 2.51/2.51 1) f9#(I0, I1, I2, I3) -> f4#(0, 0, rnd3, I3) [rnd3 = rnd3] 2.51/2.51 2) f5#(I4, I5, I6, I7) -> f4#(I4, 0, I8, I7) [I7 <= 0 /\ y1 = 1 /\ I8 = I8] 2.51/2.51 3) f5#(I9, I10, I11, I12) -> f2#(I9, I10, I11, -1 + I12) [1 <= I12] 2.51/2.51 4) f8#(I13, I14, I15, I16) -> f3#(I13, I14, I15, I16) 2.51/2.51 5) f3#(I17, I18, I19, I20) -> f8#(I17, I18, I19, I20) 2.51/2.51 6) f2#(I25, I26, I27, I28) -> f5#(I25, I26, I27, I28) 2.51/2.51 7) f4#(I29, I30, I31, I32) -> f1#(I29, I30, I31, I32) 2.51/2.51 8) f1#(I33, I34, I35, I36) -> f3#(I33, I34, I35, I36) [1 <= I35] 2.51/2.51 9) f1#(I37, I38, I39, I40) -> f2#(0, I38, I39, rnd4) [I39 <= 0 /\ I41 = 1 /\ rnd4 = rnd4] 2.51/2.51 2.51/2.51 We have the following SCCs. 2.51/2.51 { 2, 3, 6, 7, 9 } 2.51/2.51 { 4, 5 } 2.51/2.51 2.51/2.51 DP problem for innermost termination. 2.51/2.51 P = 2.51/2.51 f8#(I13, I14, I15, I16) -> f3#(I13, I14, I15, I16) 2.51/2.51 f3#(I17, I18, I19, I20) -> f8#(I17, I18, I19, I20) 2.51/2.51 R = 2.51/2.51 f10(x1, x2, x3, x4) -> f9(x1, x2, x3, x4) 2.51/2.51 f9(I0, I1, I2, I3) -> f4(0, 0, rnd3, I3) [rnd3 = rnd3] 2.51/2.51 f5(I4, I5, I6, I7) -> f4(I4, 0, I8, I7) [I7 <= 0 /\ y1 = 1 /\ I8 = I8] 2.51/2.51 f5(I9, I10, I11, I12) -> f2(I9, I10, I11, -1 + I12) [1 <= I12] 2.51/2.51 f8(I13, I14, I15, I16) -> f3(I13, I14, I15, I16) 2.51/2.51 f3(I17, I18, I19, I20) -> f8(I17, I18, I19, I20) 2.51/2.51 f6(I21, I22, I23, I24) -> f7(I21, I22, I23, I24) 2.51/2.51 f2(I25, I26, I27, I28) -> f5(I25, I26, I27, I28) 2.51/2.51 f4(I29, I30, I31, I32) -> f1(I29, I30, I31, I32) 2.51/2.51 f1(I33, I34, I35, I36) -> f3(I33, I34, I35, I36) [1 <= I35] 2.51/2.51 f1(I37, I38, I39, I40) -> f2(0, I38, I39, rnd4) [I39 <= 0 /\ I41 = 1 /\ rnd4 = rnd4] 2.51/2.51 2.51/5.49 EOF